As a player, I always wondered why there was so little online about Divination ( divination magic, etc) in roleplaying game. I'm an avid player of DD3.5 and I found a lot of "thesis" on spell casting and playing this or that but nothing that talked a lot about divination. I've read why it is hard for the player as well as for the dungeon master to use it as it is a game breaker when used properly.
So here are my advice to use divination in your game, and not only as the weird stand alone oracle that will give strange advice but actively as a player.
First, find a way to get a yes and no answer. I don't know what game you are playing but yes and no answer can be wonderful. For example, you want to search a treasure here what you do : first bring a map, then draw a line on the map, choose one side to be side A and one to be side B. Cast your divination and ask : If I would search for the treasure in side A, would I be physically closer than if I started in side B. Then you get your answer, yes or no, and it is like you had searched half of the terrain you had to search, wonderful isn't it? Sure for a dungeon master it can not be fun since the player might avoid some challenges you prepared but in the end the story will progress faster and the story, isn't this the reason why we play?
Second, cryptic divination. Those are the ones where you ask a question and you receive a cryptic answer. Usually they are not welcome by dungeon master because either they spend extra time preparing a cryptic answer or they easily give you the answer. Here I won't give you tips on asking questions ( basically you ask whatever you want and just try to understand the answer) I'll give you a tip to help your dungeon master to work with those. It is simple, give him time to prepare. You should either tell him the session before that you'll cast a divination and what you'll ask, this way he's going to be able to prepare a nice cryptic message, that will also feel like a puzzle, or do it at the end of the session and end it before receiving the answer, either way he'll have time to prepare his message and the message might be more custom to your needs while not breaking the story since the DM will have had time to prepare his answer.
Third and last : immediate divination. Those feel like flash, insight, etc, that happen just before doing an action. They help you by showing you what will happen if you do what you planned on doing. This way you can change your actions and avoid the consequence or decide that you still want to do the action but you'll prepare yourself to what you're going to receive. This one doesn't really need advice on how yo use it, you just do.
I think this sums up the main type of divination you'll find in a video game. I believe that divination might be one of the strongest kind of power ( even the strongest) because it allow you to know what will happen and prepare for it. Use it with caution and don't forget that in a roleplaying game, player and npc should all have acces to the same ressources so if you abuse it why shouldn't they?
Good talk! Have fun!